平面凸集存在最小凸生成集的充要条件

A Sufficient and Necessary Condition for the UniqueSmallest Generating Subset's Existence of a Planar Convex Set

本文在平面上解决了StevenRLay在 [1 ]中提出的开放性问题“什么样的凸集存在唯一的最小凸生成子集” ,给出并证明了“平面上的凸集存在唯一的最小凸生成子集”的一个充要条件 .同时证明了En 中的开集一定不存在最小凸生成集 .

This paper resolves partly the open problem whether there is a unique smallest subset for a convex set whose convex hull is equal to the set,which was proposed by Steven R.Lay in the material convex sets and their application.The paper provieds and proves a sufficient and necessary condition about the open problem.Moreover the paper prove the answer is negative for an open set in En.